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Trudy Inst. Mat. i Mekh. UrO RAN, 2009, Volume 15, Number 4, Pages 183–194 (Mi timm435)  

This article is cited in 2 scientific papers (total in 2 papers)

Minimax and viscosity solutions in optimization problems for hereditary systems

N. Yu. Lukoyanov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: For a dynamical system with discrete and distributed time delays, a control problem under disturbance or counteraction is considered. The problem is formalized in the context of the game-theoretical approach in the class of control strategies with memory. The problem is associated with a functional Hamilton–Jacobi type equation with coinvariant derivatives. The minimax and viscosity approaches to a generalized solution of this equation are discussed. It is shown that, under the same condition at the right endpoint, the minimax and viscosity solutions coincide, thereby uniquely defining the functional of optimal guaranteed result in the control problem

Keywords: optimal control, differential games, time-delay systems, Hamilton–Jacobi equations, minimax solution, viscosity solution.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2010, 269, suppl. 1, S214–S225

Document Type: Article
UDC: 517.977
Received: 14.04.2009

Citation: N. Yu. Lukoyanov, “Minimax and viscosity solutions in optimization problems for hereditary systems”, Trudy Inst. Mat. i Mekh. UrO RAN, 15, no. 4, 2009, 183–194; Proc. Steklov Inst. Math. (Suppl.), 269, suppl. 1 (2010), S214–S225

Citation in format AMSBIB
\Bibitem{Luk09}
\by N.~Yu.~Lukoyanov
\paper Minimax and viscosity solutions in optimization problems for hereditary systems
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2009
\vol 15
\issue 4
\pages 183--194
\mathnet{http://mi.mathnet.ru/timm435}
\elib{http://elibrary.ru/item.asp?id=12952764}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2010
\vol 269
\issue , suppl. 1
\pages S214--S225
\crossref{https://doi.org/10.1134/S0081543810060179}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84962468865}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. N. Yu. Lukoyanov, “On Hamilton–Jacobi formalism in time-delay control systems”, Tr. IMM UrO RAN, 16, no. 5, 2010, 269–277  mathnet  elib
    2. Bayraktar E., Keller Ch., “Path-Dependent Hamilton–Jacobi Equations in Infinite Dimensions”, J. Funct. Anal., 275:8 (2018), 2096–2161  crossref  mathscinet  zmath  isi  scopus
  • Trudy Instituta Matematiki i Mekhaniki UrO RAN
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